Pre-Algebra to Pre-Calculus

Transcription

1 Pre-Algebra to Pre-Calculus 11,000 free-response questions for middle and high school math This document shows the table of contents and number of questions in EducAide s database module called Pre-Alg to Pre-Calc. It is current as of December 15, 2016, though subject to change. The database is available to Problem-Attic school subscribers. For more information, please go to. Note: free-response is used broadly to mean all question types except multiple-choice. The database includes, for example, short tasks, geometry proofs, column matching, and multi-select questions. Pre-Algebra Numbers and operations Classify numbers 20 Order of operations 6 Factors and divisibility 20 Rational numbers: convert 46 Rational numbers: compare 8 Law of exponents: positive integers 30 Law of exponents: negative integers 28 Scientific notation: convert 24 Scientific notation: applications 68 Radicals: simplify 14 Radicals: operations 34 Numeric patterns 60 Geometric/visual patterns 22 Expressions, Equations, Inequalities Write expressions 20 Write equations 24 Given an equation, write a problem 12 What additional information is needed 10 Inequalities, solve and graph 12 Inequalities, applications 24 Absolute value equations 10 Properties of algebra 14 Integers and rational numbers Integers 80 Fractions 36 Decimals 84 Percent 86 Estimation 44 Averages (simple) 40 Averages (find missing value) 12 Ratios 70 Proportions 84 Average rate of change, slope/intercept 16

2 EducAide s Pre-Alg to Pre-Calc database page 2 Monomials 34 Polynomials 80 Formulas 72 Time 12 Measurement and conversion 56 Area, perimeter, volume (simple) 90 Time, distance, rate (simple) 50 Data Analysis, Probability Data analysis 66 Mean, median, mode, range 50 Make predictions 18 Probability: basic counting principle 28 Probability: single event 68 Probability: compound event 38 Probability: expected value 16 Algebra I First degree equations: applications Interest and investment (simple) 92 Number problems (simple) 128 Number problems (advanced) 74 Consecutive integers 80 Coins and stamps 48 Age problems 48 Time, distance, rate (advanced) 64 Mixture problems 68 Interest and investment (advanced) 44 Area, perimeter, volume (advanced) 72 Other first degree problems 36 Rational, Quadratic, Systems of Equations Rational equations (applications) 92 Quadratic expressions: factors, models 40 Quadratic equations: roots 78 Quadratic equations: solve 56 Quadratic equations: multiply binomials 10 Quadratic equations: applications, factorable 120 Quadratic formula: applications 80 Systems: algebraic 66 Systems: graphical 32 Systems: maximum value 12 Linear inequalities: graph 14 Systems of linear inequalities 6

3 EducAide s Pre-Alg to Pre-Calc database page 3 Functions Introduction to functions 24 Linear: applications 32 Linear: graph 10 Absolute value: properties of graphs 10 Quadratic: write equation 14 Quadratic: graph properties 70 Transformations, parent functions 56 Quadratic: applications 14 Quadratic: applications, min/max 66 Geometry Geometry: Introductory Topics Geometric terms 76 Characteristics of geometric figures 52 Naming figures 46 Identifying parts of figures 18 Intersections 28 Properties of algebra 8 Logic, forms of argument 70 Symbolic logic, truth tables 20 Logic applications 20 Angles and Parallel Lines Characteristics of angles 24 Sketching angles 8 Identifying types of angles 44 Angle measures 18 Angle addition and subtraction 26 Angle measurement problems 28 Angle bisectors 42 Complementary and supplementary angles 66 Characteristics of parallel lines 40 Tests for parallel lines 36 Angle relationships 16 Problem solving 60 Triangles and Polygons Characteristics of triangles 46 Angle measures 52 Side lengths 50 Points of concurrence 44 Supplements/complements, applications 24 Characteristics of polygons 36 Trapezoids 34 Parallelograms 44 Special parallelograms 44 Regular polygons 10

4 EducAide s Pre-Alg to Pre-Calc database page 4 Interior angles of polygons 40 Exterior angles of polygons 30 Similarity and Congruence Characteristics of similar figures 38 Tests for similarity 36 Segment proportionality 20 Triangle proportionality 48 Angle bisectors and opposite sides 10 Golden ratio problems 16 Problem solving with similar polygons 58 Characteristics of congruent polygons 22 Tests for congruence 56 Congruence statements 26 Establishing congruence 10 Corresponding parts of congruent triangles 16 Problem solving with congruence 26 Right Triangles Area Circles Geometric mean 38 Altitude to hypotenuse of right triangle 28 Pythagorean Theorem converse 22 Pythagorean Triples 12 Special right triangles: Special right triangles: Pythagorean theorem I 68 Pythagorean theorem II 80 Applications 76 Rectangles and squares 42 Area of triangles 46 Hero s Formula 28 Parallelograms 30 Area of trapezoids 40 Rhombuses 22 Other polygons 52 Ratio of area for similar polygons 14 Characteristics of circles 16 Central angles 16 Inscribed angles 68 Arcs and angles; chords, secants, and tangents 52 Chord lengths 50 Radii, diameters, and circumferences 46 Arc lengths 28 Secant and tangent lengths 54 Areas of circles 50 Areas of sectors, segments, and annuli 42

5 EducAide s Pre-Alg to Pre-Calc database page 5 Solids, Volume, and Surface Area Characteristics of solids 30 Volumes of prisms 54 Surface areas of prisms 24 Volumes of cylinders 32 Surface areas of cylinders 20 Volumes of pyramids and cones 48 Surface areas of pyramids and cones 34 Volumes of spheres and hemispheres 30 SA and cross sections of spheres/hemispheres 42 Platonic solids 28 Solids contained in solids 22 Ratio of volume for similar solids 44 Spatial reasoning 10 Coordinate Geometry Graphs of ordered pairs 14 Midpoint 64 Distance 52 Slope between 2 points 50 Points on a line 58 Equations of lines 90 Effects of change in slope and intercept 12 Parallel and perpendicular lines 74 Systems 52 Mixed practice 62 Segment lengths and shapes 42 Segment lengths and area 38 Geometric reasoning 54 Constructions, Transformations and Symmetry Characteristics of transformations 52 Transformations and the coordinate plane 78 Mapping 92 Symmetry 48 Tessellations 12 Sketching Geometric Figures 90 Constructions 72 Labeling, assumptions from drawings 16 Loci 50 Networks 20

6 EducAide s Pre-Alg to Pre-Calc database page 6 Geometric Proof Properties 28 Number properties 24 Segments 30 Angle measurement 48 Complementary and supplementary angles 42 Parallel lines 56 Triangles 30 Isosceles triangles 70 Triangle congruence (SSS/SAS/HL) 30 Triangle congruence (ASA/AAS) 24 Triangle congruence (CPCTC I) 62 Triangle congruence (CPCTC II) 52 Similarity 54 Quadrilaterals 70 Inequalities 50 Three dimensional figures 30 Circles 54 Coordinate geometry 18 Indirect proof 24 Fill-in-the-blank 54 Algebra II General Rational exponents: expressions and equations 14 Rational exponents: applications 8 Solve equations for specific variable 32 Defined operations 4 Complex Numbers 28 Non-linear Expressions and Equations Polynomials: roots 58 Polynomials: operations 58 Polynomials: factor 56 Polynomials: applications 16 Rational: simplify 20 Rational: operations 16 Rational: equations 26 Radical: equations 4 Radical: applications 14 Variation: equations 40 Variation: applications 28 Non-linear inequalities 26

7 EducAide s Pre-Alg to Pre-Calc database page 7 Systems 3+ equations/inequalities: solve equations/inequalities: applications 8 Non-linear equations: equations 38 Non-linear equations: applications 16 Non-linear inequalities: equations 8 Sequence and Series Sequences 106 Series 94 Sigma notation 24 Arithmetic and geometric means 48 Applications 68 Binomial expansion 38 Functions Conics Identify type 22 Domain and range 48 Evaluate 14 Combine and compose 12 Inverse and reciprocal 26 Effects of transformations 20 Polynomial graph properties 22 Rational graph properties 14 Radical graph properties 4 Graph, identify 22 Points on the curve 10 Write equations 82 Convert between standard and general form 18 Graph properties 52 Tangent and secants 4 Effects of transformations 8 Applications 40 Logarithmic and Exponential Convert between log and exponential form 18 Properties of logarithms 54 Exponential equations 8 Logarithmic equations 22 Applications 90

8 EducAide s Pre-Alg to Pre-Calc database page 8 Trigonometry/Pre-Calculus Right Triangle Trigonometry Trig. values: given sides 42 Trig. values: given angles 16 Find angle measures given trig. values 30 Given one trig. value, find another 10 Triangles: find sides and angles 72 Applications 50 Non-right Triangle Trigonometry Sine and cosine laws: triangles 46 Sine and cosine laws: applications 14 Area using trig values 16 Circular Trigonometry Convert degrees and radians 12 Coterminal and reference angles 12 Angle, arc length, area 6 Trig. values 18 Standard position 58 The wrapping function 6 Identities 16 Equations 6 Applications 48 Trigonometric Functions Graph properties 56 Effects of transformations 20 Equations 62 Identities 34 Applications 38 Periodic function applications 16 Polar Coordinates Convert coordinates 10 Convert equations 12 Operations 4 Introduction to Calculus Limit of a sequence 10 Slope of secant and tangent lines 14 Evaluate derivatives 38 Increasing and decreasing functions 18 Maximum and minimum values 12 Velocity and acceleration 14